TSTP Solution File: GEO007-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO007-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 94 ( 26 unt; 6 typ; 0 def)
% Number of atoms : 431 ( 85 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 536 ( 215 ~; 272 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 2 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 198 ( 184 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(e_type,type,
e: $i ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
( between(d,a,c)
<=> between(d,a,c) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
between(d,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_c) ).
tff(3,plain,
between(d,a,c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(d,a,c)
| ( a = insertion(d,c,d,a) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(d,a,c)
| ( a = insertion(d,c,d,a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(d,a,c)
| ( a = insertion(d,c,d,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(d,a,c)
| ( a = insertion(d,c,d,a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
a = insertion(d,c,d,a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
insertion(d,c,d,a) = a,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( between(insertion(d,c,d,a),e,d)
<=> between(a,e,d) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( between(a,e,d)
<=> between(insertion(d,c,d,a),e,d) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ between(a,e,d)
<=> ~ between(insertion(d,c,d,a),e,d) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ~ between(d,e,a)
<=> ~ between(d,e,a) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ between(d,e,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_not_between_d_and_a) ).
tff(21,plain,
~ between(d,e,a),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ between(U,V,W)
| between(W,V,U) )
<=> ( ~ between(U,V,W)
| between(W,V,U) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
tff(26,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,e,d)
| between(d,e,a) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,e,d)
| between(d,e,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,e,d)
| between(d,e,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,e,d)
| between(d,e,a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ between(a,e,d),
inference(unit_resolution,[status(thm)],[31,28,21]) ).
tff(33,plain,
~ between(insertion(d,c,d,a),e,d),
inference(modus_ponens,[status(thm)],[32,18]) ).
tff(34,plain,
( between(insertion(d,c,d,a),d,e)
<=> between(a,d,e) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(35,plain,
( between(a,d,e)
<=> between(insertion(d,c,d,a),d,e) ),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ between(a,d,e)
<=> ~ between(insertion(d,c,d,a),d,e) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ~ between(e,d,a)
<=> ~ between(e,d,a) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
~ between(e,d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_between_e_and_a) ).
tff(39,plain,
~ between(e,d,a),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,d,e)
| between(e,d,a) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,d,e)
| between(e,d,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,d,e)
| between(e,d,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(a,d,e)
| between(e,d,a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ between(a,d,e),
inference(unit_resolution,[status(thm)],[42,28,39]) ).
tff(44,plain,
~ between(insertion(d,c,d,a),d,e),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( between(c,insertion(d,c,d,a),e)
<=> between(c,a,e) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(46,plain,
( between(c,a,e)
<=> between(c,insertion(d,c,d,a),e) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( between(e,a,c)
<=> between(e,a,c) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
between(e,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_e) ).
tff(49,plain,
between(e,a,c),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(e,a,c)
| between(c,a,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(e,a,c)
| between(c,a,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(e,a,c)
| between(c,a,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(e,a,c)
| between(c,a,e) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
between(c,a,e),
inference(unit_resolution,[status(thm)],[52,28,49]) ).
tff(54,plain,
between(c,insertion(d,c,d,a),e),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( c = a )
<=> ( a = c ) ),
inference(commutativity,[status(thm)],]) ).
tff(56,plain,
( ( c = insertion(d,c,d,a) )
<=> ( c = a ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(57,plain,
( ( c = insertion(d,c,d,a) )
<=> ( a = c ) ),
inference(transitivity,[status(thm)],[56,55]) ).
tff(58,plain,
( ( a = c )
<=> ( c = insertion(d,c,d,a) ) ),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ( a != c )
<=> ( c != insertion(d,c,d,a) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( a != c )
<=> ( a != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
tff(62,plain,
a != c,
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
c != insertion(d,c,d,a),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
( between(c,insertion(d,c,d,a),d)
<=> between(c,a,d) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(65,plain,
( between(c,a,d)
<=> between(c,insertion(d,c,d,a),d) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(d,a,c)
| between(c,a,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(d,a,c)
| between(c,a,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(d,a,c)
| between(c,a,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(d,a,c)
| between(c,a,d) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
between(c,a,d),
inference(unit_resolution,[status(thm)],[68,28,3]) ).
tff(70,plain,
between(c,insertion(d,c,d,a),d),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ between(U,V,W)
| ~ between(U,V,X) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) ) )),
rewrite(
( ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
rewrite(
( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
rewrite(
( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).
tff(77,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),e)
| ~ between(c,insertion(d,c,d,a),d)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) )
<=> ( ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),e)
| ~ between(c,insertion(d,c,d,a),d)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),e)
| ~ between(c,insertion(d,c,d,a),d)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),e)
| ~ between(c,insertion(d,c,d,a),d)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ( c = insertion(d,c,d,a) )
| ~ between(c,insertion(d,c,d,a),d)
| ~ between(c,insertion(d,c,d,a),e)
| between(insertion(d,c,d,a),d,e)
| between(insertion(d,c,d,a),e,d) ),
inference(unit_resolution,[status(thm)],[86,80]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,70,63,54,44,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO007-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Wed Aug 31 04:32:18 EDT 2022
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------